* Last year's job: This is the most common and grammatically correct way to refer to a job held in the previous year.
* Last years' jobs: This is grammatically incorrect.
* Jobs from last year: This is another grammatically correct option, especially if you are talking about multiple jobs.
For example:
* "My last year's job was at a software company."
* "I am looking for a new job after losing my last year's job."
* "I've applied for several jobs from last year that are still open."